WASHINGTON — With broad support from Republicans and Democrats, a House committee Wednesday approved legislation to tackle the growing problem of sexual assault in the armed forces by taking away the power of military commanders to overturn convictions in rape and assault cases.

The bill passed by the House Armed Services Committee also requires that anyone found guilty of a sex-related crime receive a punishment that includes, at a minimum, a dismissal from military service or a dishonorable discharge.

“The word should go out clearly and strongly that if you commit a sexual assault in the military, you are out,” said Rep. Michael Turner, R-Ohio. Turner and Rep. Niki Tsongas, D-Mass., wrote many of the provisions in the House bill.

By stripping commanders of their longstanding authority to reverse or change court-martial convictions, lawmakers are aiming to shake up the military’s culture and give victims the confidence that if they report a crime their allegations won’t be discounted and they won’t face retaliation.

Frustration has been building on Capitol Hill for weeks over the Defense Department’s failure to staunch sexual assaults in the ranks.

The Pentagon estimated in a recent report that as many as 26,000 military members may have been sexually assaulted last year, up from an estimated 19,000 assaults in 2011, based on an anonymous survey of military personnel. While the number of sexual assaults that members of the military actually reported rose 6 percent to 3,374 in 2012, thousands of victims were still unwilling to come forward despite new oversight and assistance programs aimed at curbing the crimes, the report said.

“The military has obviously been unable to solve this problem independently,” Tsongas said.

The legislation is part of a sweeping defense policy bill that the Republican-led Armed Services Committee pulled together during a daylong session. The $638 billion measure for the fiscal year beginning Oct. 1 included $86 billion for the war in Afghanistan as well as contentious provisions on the U.S. detention facility at Guantanamo Bay, Cuba, and nuclear weapons.

The full House is expected to vote on the bill next week.

Despite the congressional clamor to cut the deficit, the committee bill rejects several Pentagon attempts to save money. It spares a version of the Global Hawk unmanned aircraft, rebuffs attempts to increase health care fees for retirees and their dependents, and opposes another round of domestic base closures.

In fact, the panel didn’t just say no to more base closings, it went as far as including a provision barring the Pentagon from even planning for another round.

That drew ridicule from Smith, who offered an amendment essentially eliminating the prohibition on the Pentagon thinking ahead. Smith said it made no sense to tie the Pentagon’s hands as it faces smaller budgets.

“I don’t think this committee has the luxury of being so darn parochial anymore, to say every single time any one of the (military) services comes into our state and says, ‘Look, we’ve got to rearrange,’ that we’re going to fight tooth-and-nail to stop them,” Smith said.

But Smith’s amendment was soundly rejected, 44-18. Several Republicans argued that they didn’t want the Pentagon wasting time planning for an effort that Congress would never accept.

The committee approved an amendment to provide $140 million as a down payment to install ground-based interceptors at a new missile defense site on the East Coast to expand the country’s defenses from a potential ballistic missile attack by Iran. The measure would require the site at a yet-to-be-determined location to be ready by 2018.

Overall, the bill fails to acknowledge the automatic, across-the-board spending cuts that Washington has grudgingly accepted. The cuts of $41 billion hit the Pentagon on March 1 and forced the military to furlough workers and scale back training.

The Pentagon faces deeper reductions in projected spending of close to $1 trillion over a decade, but the bill did not reflect that reality for next fiscal year. The Pentagon likely will have to cut $54 billion to meet the numbers dictated by the so-called sequester.

The committee’s action on sexual assaults came one day after a high-profile Senate hearing during which senators grilled military leaders about the scourge in their ranks. The leaders conceded that they have been less than diligent in dealing with the problem, but pushed back against far-reaching legislation to give the authority to level charges to a military prosecutor rather than the victim’s commander.

Military leaders are more receptive to the House provisions, would strip commanders of the discretion to reverse a court-martial ruling, except in cases involving minor offenses. Commanders also would be barred from reducing a guilty finding by a court-martial to guilty of a lesser offense.

The measure also would require that anyone found guilty of rape, sexual assault, forcible sodomy or an attempt to commit any of those offenses receive a punishment that includes a dismissal from military service or a dishonorable discharge.

The legislation eliminates the five-year statute of limitations on trial by court-martial for sexual assault and sexual assault of a child. It also establishes the authority for military legal counsel to provide legal assistance to victims of sex-related offenses and requires enhanced training for all military and civilian attorneys involved in sex-related cases.

Rep. Jackie Speier, D-Calif., applauded the committee’s action. But she said she would continue to push for even broader changes to better protect victims.

Speier has introduced separate legislation that would take the reporting and investigation of sexual assaults out of the military’s normal chain of command. The bill would create an autonomous Sexual Assault Oversight and Response Office comprised of civilian and military experts. Speier said she will offer her bill as an amendment on the House floor.

“Unless we increase the number of prosecutions and the number of convictions, they we have not achieved the goal,” she said. “We have not sanitized the military of sexual predators.”